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If f is a differentiable function, then the values x=cat which the sign of the derivative f'x changes are the locations of the local extrema of f. Use this information to find the local extrema of the functionrole="math" localid="1649873816717" f(x)=sinx. Illustrate your answer on a graph ofy=sinx.

Short Answer

Expert verified

The local extrema of the given function is at x=-1,0,1. The graph of the given function is given below,

Step by step solution

01

Step 1. Given information.

Consider the given question,

The local extrema of the function f(x)=sinx.

02

Step 2. Write the derivative of the given function.

The derivative of the given function,

f'x=cosx

For local extrema, put f'x=0. Then,

role="math" localid="1649874004201" 0=cosxx=...,-3π2,-π2,0,π2,3π2,...x=2n+1π2

Where, n is an integer.

So,

fπ2=sinπ2=0f-π2=sin-π2=-1f3π2=sin3π2=-1f-3π2=sin-3π2=1

Therefore, the required graph isy=sinx.

03

Step 3. Plot the function.

On plotting the function is given below,

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